A small object of mass m starts from rest at the position shown and slide along the frictionless loop-the-loop track of radius R. what is the smallest value of y such that object will slide without losing contact with the track ? (1) R/2, (2) R/4, (3) R, (4) 2R, (5) zero

## A small object of mass m starts from rest at the position shown and slide along the frictionless loop-the-loop track of radius R. what is the smallest value of y such that object will slide without losing contact with the track ? (1) R/2, (2) R/4, (3) R, (4) 2R, (5) zero

PHSX 220 Homework 12 D2L – Due Thursday April 13 – 5:00 pm Exam 3 MC Review Problem 1: A 1.0-kg with a velocity of 2.0m/s perpendicular towards a wall rebounds from the wall at 1.5m/s perpendicularlly away from the wall. The change in the momentum of the ball is: A. zero B. 0.5 N s away from wall C. 0.5 N s toward wall D. 3.5 N s away from wall E. 3.5 N s toward wall Problem 2: A 64 kg man stands on a frictionless surface with a 0.10 kg stone at his feet. Both the man and the person are initially at rest. He kicks the stone with his foot so that his end velocity is 0.0017m/s in the forward direction. The velocity of the stone is now: A. 1.1m/s forward B. 1.1m/s backward C. 0.0017m/s forward D. 0.0017m/s backward E. none of these Problem 3: A 2-kg cart, traveling on a rctionless surface with a speed of 3m/s, collides with a stationary 4-kg cart. The carts then stick together. Calculate the magnitude of the impulse exerted by one cart on the other: A. 0 B. 4N s C. 6N s D. 9N s E. 12N s Problem 4: A disc has an initial angular velocity of 18 radians per second. It has a constant angular acceleration of 2.0 radians per second every second and is slowing at rst. How much time elapses before its angular velocity is 18 rad/s in the direction opposite to its initial angular velocity? A. 3.0 s B. 6.0 s C. 9.0 s D. 18 s E. 36 s Problem 5: Three point masses of M, 2M, and 3M, are fastened to a massless rod of length L as shown. The rotational inertia about the rotational axis shown is: A. (ML2=2) B. (ML2) C. (3ML2)=2 D. (6ML2) E. (3ML2)=4 Problem 6: A board is allowed to pivot about its center. A 5-N force is applied 2m from the pivot and another 5-N force is applied 4m from the pivot. These forces are applied at the angles shown in the gure. The magnitude of the net torque about the pivot is: A. 0 Nm B. 5 Nm C. 8.7 Nm D. 15 Nm E. 26 Nm Problem 7: A solid disk (r=0.03 m) and a rotational inertia of 4:5×10􀀀3kgm2 hangs from the ceiling. A string passes over it with a 2.0-kg block and a 4.0-kg block hanging on either end of the string and does not slip as the system starts to move. When the speed of the 4 kg block is 2.0m/s the kinetic energy of the pulley is: A. 0.15 J B. 0.30 J C. 1.0J D. 10 J E. 20 J Problem 8: A merry go round (r= 3.0m, I =600 kgm2) is initially spinning with an angular velocity of 0.80 radians per second when a 20 kg point mass moves from the center to the rim. Calculate the nal angular velocity of the system: A. 0.62 rad/s B. 0.73 rad/s C. 0.80 rad/s D. 0.89 rad/s E. 1.1 rad/s

## PHSX 220 Homework 12 D2L – Due Thursday April 13 – 5:00 pm Exam 3 MC Review Problem 1: A 1.0-kg with a velocity of 2.0m/s perpendicular towards a wall rebounds from the wall at 1.5m/s perpendicularlly away from the wall. The change in the momentum of the ball is: A. zero B. 0.5 N s away from wall C. 0.5 N s toward wall D. 3.5 N s away from wall E. 3.5 N s toward wall Problem 2: A 64 kg man stands on a frictionless surface with a 0.10 kg stone at his feet. Both the man and the person are initially at rest. He kicks the stone with his foot so that his end velocity is 0.0017m/s in the forward direction. The velocity of the stone is now: A. 1.1m/s forward B. 1.1m/s backward C. 0.0017m/s forward D. 0.0017m/s backward E. none of these Problem 3: A 2-kg cart, traveling on a rctionless surface with a speed of 3m/s, collides with a stationary 4-kg cart. The carts then stick together. Calculate the magnitude of the impulse exerted by one cart on the other: A. 0 B. 4N s C. 6N s D. 9N s E. 12N s Problem 4: A disc has an initial angular velocity of 18 radians per second. It has a constant angular acceleration of 2.0 radians per second every second and is slowing at rst. How much time elapses before its angular velocity is 18 rad/s in the direction opposite to its initial angular velocity? A. 3.0 s B. 6.0 s C. 9.0 s D. 18 s E. 36 s Problem 5: Three point masses of M, 2M, and 3M, are fastened to a massless rod of length L as shown. The rotational inertia about the rotational axis shown is: A. (ML2=2) B. (ML2) C. (3ML2)=2 D. (6ML2) E. (3ML2)=4 Problem 6: A board is allowed to pivot about its center. A 5-N force is applied 2m from the pivot and another 5-N force is applied 4m from the pivot. These forces are applied at the angles shown in the gure. The magnitude of the net torque about the pivot is: A. 0 Nm B. 5 Nm C. 8.7 Nm D. 15 Nm E. 26 Nm Problem 7: A solid disk (r=0.03 m) and a rotational inertia of 4:5×10􀀀3kgm2 hangs from the ceiling. A string passes over it with a 2.0-kg block and a 4.0-kg block hanging on either end of the string and does not slip as the system starts to move. When the speed of the 4 kg block is 2.0m/s the kinetic energy of the pulley is: A. 0.15 J B. 0.30 J C. 1.0J D. 10 J E. 20 J Problem 8: A merry go round (r= 3.0m, I =600 kgm2) is initially spinning with an angular velocity of 0.80 radians per second when a 20 kg point mass moves from the center to the rim. Calculate the nal angular velocity of the system: A. 0.62 rad/s B. 0.73 rad/s C. 0.80 rad/s D. 0.89 rad/s E. 1.1 rad/s

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The Rocket Equation The Tsiolovsky Rocket Equation describes the velocity that results from pushing matter (exploding rocket fuel) in the opposite direction to the direction you want to travel. This assignment requires you to do basic calculation using the Tsiolovsky Rocket Equation : v[t] = eV Log M M – bR t  – g t The parameters used are : ◼ eV exhaust velocity (m/s) ◼ pL payload (kg) ◼ fL fuel load (kg) ◼ M is the mass of the rocket (pL+fL, kg) ◼ bR the burn rate of fuel (kg/s) ◼ g the force due to gravity ms2 The variables calculated are : h(t) the height of the rocket at time t (m) v(t) the velocity of the rocket at time t (m/s) m(t) the mass of the rocket at time t (kg) Questions Question 1 (1 mark) Write an expression corresponding to the Tsiolovsky rocket equation and use integrate to find a function to describe the height of the rocket during fuel burn. Question 2 (2 marks) The fuel burns at a constant rate. Find the time (t0), velocity (vmax), and height (h0) of the rocket when the fuel runs out (calculate the time when the fuel runs out, and substitute this into the height Printed by Wolfram Mathematica Student Edition and velocity equations). Question 3 (2 marks) The second phase is when the only accelaration acting on the rocket is from gravity. This phase starts from the height and velocity of the previous question, and the velocity is given by the projectile motion equation, v(t) = vmax – g (t – t0). Use Solve to find the time when this equation equals 0. This will be the highest point the rocket reaches before returning to earth. Question 4 (1 marks) Integerate the projectile motion equation and add h0 to find the maximum height the rocket reaches. Question 5 (1 marks) Use Solve over the projectile motion equation to find the time when the height is 0. 2 assignment4.nb Printed by Wolfram Mathematica Student Edition

## The Rocket Equation The Tsiolovsky Rocket Equation describes the velocity that results from pushing matter (exploding rocket fuel) in the opposite direction to the direction you want to travel. This assignment requires you to do basic calculation using the Tsiolovsky Rocket Equation : v[t] = eV Log M M – bR t  – g t The parameters used are : ◼ eV exhaust velocity (m/s) ◼ pL payload (kg) ◼ fL fuel load (kg) ◼ M is the mass of the rocket (pL+fL, kg) ◼ bR the burn rate of fuel (kg/s) ◼ g the force due to gravity ms2 The variables calculated are : h(t) the height of the rocket at time t (m) v(t) the velocity of the rocket at time t (m/s) m(t) the mass of the rocket at time t (kg) Questions Question 1 (1 mark) Write an expression corresponding to the Tsiolovsky rocket equation and use integrate to find a function to describe the height of the rocket during fuel burn. Question 2 (2 marks) The fuel burns at a constant rate. Find the time (t0), velocity (vmax), and height (h0) of the rocket when the fuel runs out (calculate the time when the fuel runs out, and substitute this into the height Printed by Wolfram Mathematica Student Edition and velocity equations). Question 3 (2 marks) The second phase is when the only accelaration acting on the rocket is from gravity. This phase starts from the height and velocity of the previous question, and the velocity is given by the projectile motion equation, v(t) = vmax – g (t – t0). Use Solve to find the time when this equation equals 0. This will be the highest point the rocket reaches before returning to earth. Question 4 (1 marks) Integerate the projectile motion equation and add h0 to find the maximum height the rocket reaches. Question 5 (1 marks) Use Solve over the projectile motion equation to find the time when the height is 0. 2 assignment4.nb Printed by Wolfram Mathematica Student Edition

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COMP 4440/5440 – Dr. Erdemir Mobile Robotics Project (DUE 12/02/2015) HONOR CODE I pledge my honor that I have neither given nor received aid on this work. Do not sign until after you have completed your assignment. Name: Signature: 1. (Prerequisite) Given the asset package (it is in mytsu under assignments folder) download it, open a new project (don’t double click on the file, it won’t open), go to Assets/Import Package/Custom Package, select the asset package given to you (project.unitypackage). After the import is completed, you will see main scene in the assets folder of your project. Double click on it, and choose “Don’t Save” option if it asks for save. 2. Print this page and attach it to your code and your snapshot of your final scene (5 points) 3. After the class starts, instructor will come next to you and you are supposed to show him your code running (10 points) 4. When you run the code you will see, your robot (red cube that we used in the class) is trying to reach the targets but it can’t due to an obstacle between your robot and the targets. Write a code that makes this robot to avoid from the obstacles and reach the targets. Your code will read the collision and intelligently avoid from other moving robots and fixed obstacles and get the three targets. (50 points) 5. Maximum time is 2 minutes, your robot shall get the targets in 2 minutes (10 points) 6. Your robot shall escape from the blue robot and not collide them. (10 Points) 7. Anything extra (up to 20 points) ? Moving objects, new sensor, Artificial Intelligence or other techniques. 8. YOU CAN NOT USE TRANSLATE FUNCTION. USE ONLY AddRelativeForce FUNCTION IN THE FORWARD DIRECTION AS ALL THE MOBILE ROBOTS WORK.

## COMP 4440/5440 – Dr. Erdemir Mobile Robotics Project (DUE 12/02/2015) HONOR CODE I pledge my honor that I have neither given nor received aid on this work. Do not sign until after you have completed your assignment. Name: Signature: 1. (Prerequisite) Given the asset package (it is in mytsu under assignments folder) download it, open a new project (don’t double click on the file, it won’t open), go to Assets/Import Package/Custom Package, select the asset package given to you (project.unitypackage). After the import is completed, you will see main scene in the assets folder of your project. Double click on it, and choose “Don’t Save” option if it asks for save. 2. Print this page and attach it to your code and your snapshot of your final scene (5 points) 3. After the class starts, instructor will come next to you and you are supposed to show him your code running (10 points) 4. When you run the code you will see, your robot (red cube that we used in the class) is trying to reach the targets but it can’t due to an obstacle between your robot and the targets. Write a code that makes this robot to avoid from the obstacles and reach the targets. Your code will read the collision and intelligently avoid from other moving robots and fixed obstacles and get the three targets. (50 points) 5. Maximum time is 2 minutes, your robot shall get the targets in 2 minutes (10 points) 6. Your robot shall escape from the blue robot and not collide them. (10 Points) 7. Anything extra (up to 20 points) ? Moving objects, new sensor, Artificial Intelligence or other techniques. 8. YOU CAN NOT USE TRANSLATE FUNCTION. USE ONLY AddRelativeForce FUNCTION IN THE FORWARD DIRECTION AS ALL THE MOBILE ROBOTS WORK.

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